[naasking]

Verdex's explanation is detailed but too long IMO. The short version is that ADTs/sum types formally correspond to the OR-logical connective, and records/product types formally correspond to AND-logical connective. I think you'd be hard-pressed to argue that people don't think in terms of "X AND Y OR Z". These are core primitives of any kind of reasoning.

[taeric]

I can easily argue that people don't think in terms of boolean logic. For one, the evidence seems as strong that people generally think backwards from the answer far more than they do forwards from the ingredients. This is often why new things are so long to be discovered. It isn't that people couldn't have gotten there, but they didn't know to go for it.

For two, addition is a wildly disparate thing everywhere we use it. We like to joke that computers made that hard, but literally half of intro chemistry is learning how to get thing to add together in a meaningful way, no? Balancing a chemical equation is a thing.

[naasking]

> For one, the evidence seems as strong that people generally think backwards from the answer far more than they do forwards from the ingredients.

Logic doesn't really have a direction, it works backwards or forwards. Even if you're solving a system "backwards", whatever that means, you still have to satisfy all of the necessary AND and OR constraints for a solution to be valid, so you're effectively still building ADTs or records just using a different evaluation order.

[taeric]

And this logic is how folks convince themselves that ball players are doing trigonometry when playing. It is just wrong.

You can /model/ it that way. But you are making a symbolic model to justify how a solution is reached.

Now, it can be frustrating to consider that this model could produce an agent that is better at the ball game than the players. But it is silly to think that means you have mirrored them.

[naasking]

> And this logic is how folks convince themselves that ball players are doing trigonometry when playing. It is just wrong.

You're attempting a sleight of hand here by saying "they're" not "doing trig". Clearly they are not doing anything like that consciously, but equally clearly some part of their brain is triangulating objects and predicting trajectories based on gradients, meaning that part is "doing trig and calculus" subconsciously. What else does it mean to "do something" if not "process X is isomorphic to process Y"?

> You can /model/ it that way. But you are making a symbolic model to justify how a solution is reached.

I really don't understand what you think people are doing when they're compiling a grocery list. They're clearly thinking, "I need x AND y OR I can substitute z".

Or if they're planning to paint their fence, they're thinking, "I need paint AND brushes AND I have to start before lunch OR I won't finish before dinner".

[taeric]

No. You are confusing the model for the reality. Again, our model may lead to a more impressive reality, but ball players are not doing trig. They are almost certainly simulating things, but that does not require trig. Indeed, it only loosely requires math. Models can be very informal with loose approximations.

You seem to think I have to prove your model false to show others don't do that. But I am specifically not claiming your model is false. I'm saying folks don't think that way, necessarily. For example, many build lists for shopping that they were taught. Not that they reasoned.

[naasking]

The ability to build lists requires reasoning. It requires enumeration, inclusion/exclusion conditions, and stop conditions, which necessarily requires logic. This argument is pointless, you go on believing that some people can't use basic logical connectives, I'm sure next you'll say they can't even count.

[samatman]

> Logic doesn't really have a direction, it works backwards or forwards.

Implication is one of the primitives in logic, and gives us several of the classic logical fallacies: affirming the consequent, denying the antecedent, fallacy of the converse, and fallacy of the inverse.

All of which are examples of trying to work logic as though it doesn't have a direction.

[naasking]

Implication is not primitive, "x->y" is reducible to "not(x) or y". None of those fallacies derive from a lack of direction, but from not being invalid logical deductions.